Quantum random walks and thermalisation II

TL;DR

This paper establishes a convergence theorem for quantum random walks with particles in any normal state, extending previous models and characterizing the limiting quantum stochastic processes under various conditions.

Contribution

It generalizes previous results on quantum random walks by providing a unifying convergence theorem applicable to arbitrary normal states and characterizes the limiting processes.

Findings

Unified convergence theorem for quantum random walks.

Necessary and sufficient conditions for limiting processes to be isometric, co-isometric, or unitary.

Extension of previous models to more general particle states.

Abstract

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc. (2) 81, 412-434; 2010, Comm. Math. Phys. 300, 317-329). When the random-walk generator acts by ampliation and multiplication or conjugation by a unitary operator, necessary and sufficient conditions are given for the quantum stochastic cocycle which arises in the limit to be driven by an isometric, co-isometric or unitary process.